My professor in lecture yesterday said that if a set is closed and bounded in a metric space it doesn't necessarily imply that it is compact. If X = R^n, then it does happen to be true, however. I was trying to construct an example, but I am getting confused. If I let X = R, and Y = (0,1) where Y is a subspace of X, then A = (0,1/2] is closed and bounded in Y. However, from where do I choose the open cover? That is, open relative to X or Y? I know in this case it won't make a difference, but maybe in differently chosen X, Y and A it might. I guess this is a matter of definition, but would like some help.(adsbygoogle = window.adsbygoogle || []).push({});

Thanks a lot.

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Metric Spaces and Compactness

Loading...

Similar Threads - Metric Spaces Compactness | Date |
---|---|

Visualizing the space and structure described by a metric | Feb 17, 2016 |

How to draw a 2D space in 3D Euclidean space by metric tensor | Oct 24, 2014 |

Problem about taking measurements in flat metric spaces | Apr 28, 2014 |

Compact Set in Metric Space | Oct 24, 2010 |

Compactness and Metric Spaces | Sep 29, 2010 |

**Physics Forums - The Fusion of Science and Community**